For an optical fiber distribution application, optical fibers of an optical fiber cable are usually spread through an optical fiber distribution box. Referring to FIG. 1, a conventional optical fiber distribution box 1 includes a mounting plate 11 and a housing 123. The mounting plate 11 is formed with four threaded hoes 110. The housing 123 is disposed on the mounting plate 11, and cooperates therewith to define a space therebetween, and is formed with an inlet 121 and a plurality of outlets 122. The inlet 121 permits an optical fiber cable 131 to extend therethrough into the space and the outlets 122 permit bundles of optical fibers 132 of the optical fiber 131 to extend respectively therethrough out of the space 110. The conventional optical fiber distribution box 1 is usually mounted on a wall using four screws (not shown) extending respectively into the threaded holes 110. However, it is relatively difficult to mount the conventional optical fiber distribution box 1 on a non-flat surface of an object. Thus, the applicable range for the conventional optical fiber distribution box to be mounted to objects having different shapes is limited.